Question

7
Find the points which divide the line segment joining A( 4,0) and B(0,6) into four equal
parts​

Answer 1

GiveN :-

• Two points A(4,0) and B(0,6) is given to us .

To FinD:-

• The points which divides the line joining the two points in four equal parts .

SolutioN :-

Basically here we can use the midpoint formula to find the midpoint of the points given . Then we can find the midpoint of the two parts which is divided by the midpoint of (4,0) & (0,6).

$\red{\bigstar}\underline{\textsf{ Finding the midpoint of (4,0) and (0,6) :- }}$

$\sf:\implies \pink{ Midpoint_{(x,y)}= \bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)} \\\\\sf:\implies M = \bigg(\dfrac{4+0}{2} , \dfrac{0+6}{2}\bigg)\\\\\sf:\implies M = \bigg(\dfrac{4}{2},\dfrac{6}{2}\bigg)\\\\\sf:\implies \underset{\blue{\sf First \ Point }}{\underbrace{\boxed{\pink{\frak{ Point_1 = (2,3) }}}}}$

$\rule{200}2$

$\red{\bigstar}\underline{\textsf{ Finding the midpoint of (4,0) and (2,3) :- }}$

$\sf:\implies \pink{ Midpoint_{(x,y)}= \bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)} \\\\\sf:\implies M = \bigg(\dfrac{4+2}{2} , \dfrac{0+3}{2}\bigg)\\\\\sf:\implies M = \bigg(\dfrac{6}{2},\dfrac{3}{2}\bigg)\\\\\sf:\implies \underset{\blue{\sf Second \ Point }}{\underbrace{\boxed{\pink{\frak{ Point_2= (3,1.5) }}}}}$

$\rule{200}2$

$\red{\bigstar}\underline{\textsf{ Finding the midpoint of (0,6) and (2,3) :- }}$

$\sf:\implies \pink{ Midpoint_{(x,y)}= \bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)} \\\\\sf:\implies M = \bigg(\dfrac{0+2}{2} , \dfrac{6+3}{2}\bigg)\\\\\sf:\implies M = \bigg(\dfrac{2}{2},\dfrac{9}{2}\bigg)\\\\\sf:\implies \underset{\blue{\sf Third \ Point }}{\underbrace{\boxed{\pink{\frak{ Point_3 = (1,4.5) }}}}}$

$\rule{200}2$

$\sf\twoheadrightarrow\orange{ Required\ Points = (2,3) \:\: \& (3,1.5)\:\:\& (1,4.5) }$